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Ready Classroom Mathematics - Grade 4

Curriculum Associates | Fourth Grade

Alignment: Overall Summary

The instructional materials reviewed for Ready Classroom Mathematics Grade 4 meet expectations for Alignment to the CCSSM. The materials meet the expectations for Focus and Coherence by assessing grade-level content, spending the large majority of instructional time on major work of the grade, and they are coherent with the progressions of the standards, making meaningful connections between supporting and major work of the grade, are viable for a school year, and present all students with opportunities to engage in extensive work with grade level problems to meet the full intent of grade level standards. The materials meet the expectations for Rigor and Mathematical Practices as they meet the expectations for Rigor and Balance and meet the expectations for Practice-Content Connections. The materials balance the rigorous expectations of the Standards, and they attend to Practice-Content Connections, addressing all of the Mathematical Practice Standards; however, there are instances where these are over-identified.

The Report

Gateway One

Focus & Coherence

Meets Expectations

The instructional materials for Ready Classroom Mathematics Grade 4 meet expectations for focusing on the major work of the grade and are coherent with the Standards. The materials do not assess topics before the grade-level, spend at least 65% of class time on the major clusters of the grade, and are coherent and consistent with the Standards.

Criterion 1a

Materials do not assess topics before the grade level in which the topic should be introduced.

The instructional materials reviewed for Ready Classroom Mathematics Grade 4 meet expectations for not assessing topics before the grade level in which the topic should be introduced. Overall, the materials assess grade-level content and, if applicable, content from earlier grades.

Indicator 1a

The instructional material assesses the grade-level content and, if applicable, content from earlier grades. Content from future grades may be introduced but students should not be held accountable on assessments for future expectations.

In i-Ready, Teach and Assess, Ready Classroom Mathematics, there are two versions of Unit Assessments: Form A and Form B for each unit. Form A assessments are editable. Form A assessments include a standards correlation chart, DOK levels, as well as a correlation to the lesson/s related to each assessment item. Form B assessments do not include this feature. In addition, in i-Ready, Teach and Assess, Assessments, Comprehension Checks are also available and can be used as an alternative to print mid- and end-unit assessments. Probability, statistical distributions, similarities, transformations, and congruence do not appear in the assessments.

Examples of assessment items from the Classroom Resources aligned to grade-level standards include:

In Unit 3, Assess, End of Unit Assessment, Form B, Item 2 states, “A rectangle that is 9 inches long has an area of 72 square inches. What is the perimeter of the rectangle, in inches? Show your work.” (4.MD.A.3)

In Unit 4, Assess, End of Unit Assessment, Form A, Item 7 states, “Write 8/100 as a decimal. Record your answer on the grid. Then fill in the bubbles.”(4.NF.C.6 )

In Unit 5, End of Unit Assessment, Item 11 states, “Erin is drawing a diagram of a door opening. She wants the door opening in the diagram to have a 150° angle. Draw a 150° angle. Label the angle in degrees. Show your work.” (4.G.1)

Examples of assessment items from the Assess and Teach aligned to Grade 4 CCSS include:

In Comprehension Checks, Comprehension Checks Details, Unit 1, Item 9 states, “Yelena takes 27,601 steps in one day. Round 27,601 to each given in the chart. Enter your answers in the boxes. (boxes state, ‘to the nearest ten thousand, to the nearest thousand, to the nearest hundred, to the nearest ten.’” (4.NBT.A.3)

In Comprehension Check, Comprehension Checks Details, Mid-Unit 2 (Lessons 6-8), Item 8 states, “What do all of the numbers below have in common? 7, 14, 21, 28, 35 Choose all the correct answers.” The multiple choice answers are: They have 7 as a factor, They are multiples of 7, They are factors of 7, They have seven factors, They are multiples of 14. (4.OA.4)

Criterion 1b

The instructional materials for Ready Classroom Mathematics Grade 4 meet the expectations for students and teachers using the materials as designed and devoting the majority of class time to the major work of the grade. Overall, instructional materials spend at least 65% of class time on the major clusters of the grade.

Indicator 1b

Instructional material spends the majority of class time on the major cluster of each grade.

The instructional materials reviewed for Ready Classroom Mathematics Grade 4 meet expectations for spending a majority of instructional time on major work of the grade.

The approximate number of units devoted to major work of the grade (including assessments and supporting work connected to the major work) is 4 out of 5, which is approximately 80%.

The number of lessons devoted to major work of the grade (including assessments and supporting work connected to the major work) is 32 out of 39, which is approximately 82%.

The number of days devoted to major work (including assessments and supporting work connected to the major work) is 125 out of 154, which is approximately 82%.

An instructional day level analysis is most representative of the materials because the number of sessions within each topic and lesson can vary and each lesson includes specific objectives aligned to standards. When reviewing the number of instructional days for Ready Classroom Mathematics Grade 4 materials, approximately 82% of the days are focused on the major work of the grade.

Criterion 1c - 1f

Coherence: Each grade's instructional materials are coherent and consistent with the Standards.

The instructional materials reviewed for Ready Classroom Mathematics Grade 4 meet the expectations for being coherent and consistent with the Standards. Overall, the instructional materials connect supporting content to enhance focus and coherence, are consistent with the progressions of the standards, foster connections at a single grade, where appropriate, and include extensive work with grade level problems to meet the full intent of grade-level standards.

Indicator 1c

Supporting content enhances focus and coherence simultaneously by engaging students in the major work of the grade.

The instructional materials reviewed for Ready Classroom Mathematics Grade 4 meet expectations that supporting work enhances focus and coherence simultaneously by engaging students in the major work of the grade. Supporting standards are used to support major work of the grade and often appear in lessons with connections to the major work of the grade.

Throughout the materials, supporting standards/clusters are connected to the major standards/clusters of the grade. The following are examples of the connections between supporting work and major work in Classroom Resources:

In Lesson 13, Session 3, supporting standard 4.MD.1 connects to major work standard 4.NBT.5 as students solve, “Julie makes 4 liters of orange juice. How many milliliters of orange juice does Juile make?.” Students demonstrate an understanding of conversion related to the supporting standard, 4.MD.1 by applying multiplication strategies to find their answer.

In Lesson 22, Session 4, students make line plots and solve word problems about data (supporting standard 4.MD.4) using addition and subtraction of fractions with like denominators (4.NF.3c and 4.NF.3d). Students are given a line plot with dragonfly lengths displayed in inches as mixed numbers and answer questions. For example the materials state, “What is the difference between the lengths of the longest and the shortest dragonfly?”

In Lesson 28, Session 2, standard 4.MD.2 supports major work standard 4.OA.3 as students solve word problems about money and time using fractions and whole numbers. The materials state, “Sadie spends $$1\frac {1}{2}$$ hours doing homework. She plays outside for 20 minutes and practices the piano for a quarter of an hour. How many more minutes does Sadie spend doing homework than practicing the piano and playing outside?

Indicator 1d

The amount of content designated for one grade level is viable for one school year in order to foster coherence between grades.

The instructional materials reviewed for Ready Classroom Mathematics Grade 4 meet expectations that the amount of content designated for one grade level is viable for one year.

As designed, the instructional materials can be completed in 165 days consisting of:

There are 130 lesson days.

There are 9 days for unit assessments, 6 days for i-Ready diagnostic assessments, and 5 days review, for a total of 20 days.

There are 10 days for Math in Action activities.

There are 5 days dedicated to lesson 0 at the beginning of the school year to set up instructional routines with students that will be used throughout the year.

According to Ready Classroom Mathematics Implementation, sessions are designed to be 45-60 minutes in length. Pacing information from the publisher regarding viability for one school year can be found in the document titled “Yearly Pacing” found in the “Program Implementation” tab on the home page for each grade level. The “Yearly Pacing” includes a list of units, lessons within each unit, and the number of days each lesson encompasses, a note that lessons are 45-60 minutes in length and number of days for assessments. Pacing information is also verified in the “Classroom Resources” tab in each unit for each lesson in the “Lesson Overview and Family Connection” that includes a “Lesson Pacing Guide” with more detailed information that lists sessions and minutes for each lesson.

Indicator 1e

Materials are consistent with the progressions in the Standards
i. Materials develop according to the grade-by-grade progressions in the Standards. If there is content from prior or future grades, that content is clearly identified and related to grade-level work
ii. Materials give all students extensive work with grade-level problems
iii. Materials relate grade level concepts explicitly to prior knowledge from earlier grades.

The instructional materials reviewed for Ready Classroom Mathematics Grade 4 meet expectations for the materials being consistent with the progressions in the Standards. Content from prior grades is identified and connected to grade-level work, and students are given extensive work with grade-level problems. ​

Overall, the materials develop according to the grade-by-grade progressions in the standards and prior year content is identified as prerequisite skills at the lesson level. In the Unit Overview, the materials include a Learning Progression which clearly identifies the lessons in prior years that contain skill students would connect to the current unit of instruction. For example, in Unit 3, Lesson 16, Find Perimeter and Area (4.MD.3), builds from Grade 3, Lesson 14, 15, and 32, and leads to Grade 5, Lessons 1 and 2 (Volume). In addition to the lesson description and standard correlation, teachers can find a Unit Flow and Learning Progression video which highlight how concepts in this unit progress through grade levels.

The materials give all students extensive work with grade-level problems. Units consist of lessons, which are designed to last between three and five days. Within each lesson, days are broken into Explore, Develop, and Refine sessions. Develop and Refine sessions have ample practice problems for students to understand and apply concepts, and Develop sessions also include Fluency and Skills Practice pages. Each unit also includes a Math in Action lesson, which provides further work with grade-level problems over 2 days. In addition, each lesson includes math center activities and enrichment activities, which both provide more work with grade level concepts. For example:

Lesson 8 is focused on 4.OA.B.4. In Session 1, Explore, students look back at previous learning with multiplication facts. In Sessions 2, 3, and 4, Develop, students use pictures, number lines, and other models to develop their understanding of factors and multiples. Fluency and Skills Practice pages accompany each of these Develop Sessions. In Session 5, Refine, students are presented with problems for practice and application of this skill. Math in Action, a two day problem solving lesson, provides further practice with these concepts.

Lesson 16, Math in Action, focuses on 4.MD.A (Solve problems involving measurement and conversion of measurements from a larger unit to a smaller unit). Over the two sessions, students solve increasingly complex problems applying their knowledge of measurement. In Session 1, students study the following example problem and solution, “The zoo is planning to build a new area for birds. The zoo is going to use recycled materials. There will be three different-size rectangular cages as shown below. Beau needs to find a possible length and width for the rectangular floor for each size cage. What is the possible length, width, and perimeter for each cage’s floor?” Students evaluate the sample solution and try another approach, discussing different models and strategies to solve the problem. In Session 2, students persevere by building on the first problem. The materials state, “Beau’s report about recycling was very popular, He decides to write a similar report about recycling rainwater. He will post both reports on the bulletin board at the Community Center. Here is some information Beau found about this topic. What should Beau include in his report.”

In Lesson 20, students learn to add and subtract fractions 4.NF.3 (Understand a fraction a/b with a>1 as a sum of the fractions 1/b). In Session 1, Explore, students solve problems such as, “Maria, Jon, and Kara share a set of 10 animal stickers. Maria gets 2 stickers, Jon gets 4 stickers, and Kara gets the rest of the stickers. What fraction of the stickers does Kara get?” In Session 2, Develop, students develop an understanding adding fractions. Session 3, Develop focuses on subtracting fractions. In Session 4, students decompose fractions, and in Session 5, students refine their understanding of adding and subtracting fractions.

The instructional materials explicitly connect prior learning to grade-level content. In the Lesson Overview, the Learning Progression identifies the mathematics taught in earlier grades or earlier in the grade, and connects it with the mathematics in the lesson. In Small Group Differentiation, Prepare, there is a link to Prerequisite Lessons. The Family Letter can also contain information on the learning progressions for students. For example:

In Lesson 7, the Lesson Overview identifies Grade 3, Lessons 12, 17, and 18 as prerequisites for learning. Grade 3, Lesson 12 focuses on multiplication facts, while Lessons 17 and 18 center around one-step word problems. In Grade 4, Lesson 7, students build upon this learning from Grade 3, as they work on more complex multiplication and division problems.

In Lesson 18, Lesson Overview, the Family Connection states, “In Grade 3 students used models to compare two fractions with the same numerator or the same denominator by reasoning about their size.” Information is given about the Grade 4 lesson, and then reads, “In grade 5 students will apply their understanding of fraction comparison when they learn to compare decimals.”

In Lesson 21, Lesson Overview, Prerequisite Skills include, “Understand addition as joining parts. Understand subtraction as separating parts. Write whole numbers as fractions. Add and subtract fractions that have the same denominator. Decompose a fraction as a sum of fractions with the same denominator.” In Small Group Differentiation, Prepare, Ready Prerequisite Lesson is identified as Grade 3, Lesson 21.

Indicator 1f

Materials foster coherence through connections at a single grade, where appropriate and required by the Standards
i. Materials include learning objectives that are visibly shaped by CCSSM cluster headings.
ii. Materials include problems and activities that serve to connect two or more clusters in a domain, or two or more domains in a grade, in cases where these connections are natural and important.

The instructional materials reviewed for Ready Classroom Mathematics Grade 4 meet expectations that materials foster coherence through connections at a single grade, where appropriate and required by the Standards. Overall, the materials include lesson objectives that are visibly shaped by CCSSM cluster headings.

The instructional materials identify a Learning Objectives in each Lesson Overview, and in the Student Workbook, Learning Targets are provided for students. Examples of lesson objectives that are visibly shaped by CCSSM cluster headings in Classroom Resources include:

In Student Workbook, Lesson 2, the Learning Target states, “Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form. Compare two multi-digit numbers based on the meaning of the digits in each place, using >, =, and < symbols to record the results of comparisons.” This learning target aligns with 4.NBT.A (Generalize place value understanding and properties of operations to perform multi-digit arithmetic).

In Lesson 4, Lesson Overview, one of the Learning Objectives states, “Use place-value strategies to add two or more multi-digit whole numbers.” This lesson objective is shaped by standard cluster 4.NBT.B which states, “Use place value understanding and properties of operations to perform multi-digit arithmetic.”

In Student Workbook, Lesson 26, the Learning Target states, “Use decimal notation for fractions with denominators 10 or 100.” The Lesson 27 Learning Target is to “compare two decimals to hundredths by reasoning about their size. Recognize that comparisons are valid only when two decimals refer to the same whole.” These learning targets align with 4.NF.C, understand decimal notation for fractions and compare decimals.

There are many instances of problems and activities within the materials that serve to connect two or more clusters in a domain or two or more domains in a grade in Classroom Resources. For example:

In Unit 4, Math in Action: Use Fractions and Decimals, Session 1 connects clusters 4.NF.A (Extend understanding of fraction equivalence and ordering) to 4.NF.C (Understand decimal notation for fractions, and compare decimal fractions), as students solve problems using both fractions and decimals. The materials state, “Luna made these notes after she made a sand art design in a 2- cup jar. ‘I used a glass jar that holds 2 cups. I used less than 1 cup of yellow sand. I filled less than 0.4 of the jar with pink sand. I filled more than 0.2 of the jar with purple sand.’ Luna wants to write specific instructions for making the same kind of design that would work for a jar of any size. Find fractions or decimals to tell exactly what part of each jar to fill with pink, purple, and yellow sand. Write instructions using those numbers.”

In Lesson 11, Session 1 connects 4.NBT.B (Use place value understanding and properties of operations to perform multi-digit arithmetic) and 4.NBT.A (Generalize place value understanding for multi-digit whole numbers), as students solve, “You can use arrays, area models, and partial products to break apart numbers to help you multiply. The array at the right uses base ten blocks to show 3 x 157. Part A: Write 157 in expanded form. Part B: Fill in the blanks below to show how to find 3 x 157. 3 x 157 = (3x ____) + (3 x ____) + (3 x ____).”

In Lesson 9, Session 2 connects 4.OA.C (Generate and analyze patterns) and 4.OA.B (Gain familiarity with factors and multiples), as students given multiples of 3 and asked to “describe the pattern of 3, 6, 9, 12, 15, 18.”

Gateway Two

Rigor & Mathematical Practices

Meets Expectations

The instructional materials reviewed for Ready Classroom Mathematics Grade 4 meet the expectations for alignment with the Standards’ expectations for rigor and the mathematical practices. The instructional materials attend to each of the three aspects of rigor individually, and also attend to balance among the three aspects. The instructional emphasizes mathematical reasoning, and attends to the full intent of each practice standard; however, there are instances where the practice standards are overidentified.

Criterion 2a - 2d

Rigor and Balance: Each grade's instructional materials reflect the balances in the Standards and help students meet the Standards' rigorous expectations, by helping students develop conceptual understanding, procedural skill and fluency, and application.

The instructional materials reviewed for Ready Classroom Mathematics Grade 4 meet the expectations for reflecting the balances in the Standards, and helping students to meet the Standards’ rigorous expectations by helping students develop and demonstrate conceptual understanding, procedural skill and fluency, and application. The instructional materials develop conceptual understanding of key mathematical concepts, give attention throughout the year to procedural skill and fluency, spend sufficient time working with engaging applications, and do not always treat the three aspects of rigor together or separately.

Indicator 2a

Attention to conceptual understanding: Materials develop conceptual understanding of key mathematical concepts, especially where called for in specific content standards or cluster headings.

The instructional materials reviewed for Ready Classroom Mathematics Grade 4 meet expectations that the materials develop conceptual understanding of key mathematical concepts, especially where called for in specific standards or cluster headings.

Lessons are designed to support students to explore and develop conceptual understanding of grade-level mathematics. For example, students develop conceptual understanding:

In Lesson 8 Session 3, Develop, students model problems using both pictures and arrays to determine the factors of a number. The teacher’s guide prompts teachers to ask students the following questions, “Where does your model show the total number of cars in each arrangement of cars? The number of cars in each same-sized row? The number of rows?” (4.OA.4)

In Lesson 11, Session 2, Develop, students are shown models of base ten blocks and partial products to multiply. Teachers are instructed, “Compare and connect the different representations and have students identify how they are related.” Teachers ask, “Where does your model show the number of hundreds, tens and ones in 254? the multiplication of each place value by 3? the product?” These questions help students build conceptual understanding of multiplication by one-digit numbers (4.NBT.5)

In Lesson 12, Session 2, Develop, Try It, students develop conceptual understanding of multiplying two two-digit numbers, using strategies based on place value and the properties of operations (4.NBT.5), as students are presented with the problem “16 x 28” and shown solutions using an area model and partial products. Students are then asked to reflect as to how the partial products method relates to the area model method.

In Lesson 18, Session 2, Develop, Try It states, “A grasshopper weighs $$\frac {2}{100}$$ of an ounce. A beetle weighs $$\frac {8}{10}$$ of an ounce. Which weighs more?” Students are prompted to use a math toolkit in the margin which lists, “number lines, hundredths grids, tenth grids, index cards, and fraction models.” (4.NF.2)

In the Student Worktext and during Interactive Practice, students have opportunities to independently demonstrate conceptual understanding. For example:

In Unit 1, Math in Action, Session 1, students work independently to develop a conceptual understanding of place value and expanded form as they solve “Yearly Blog Visits.” Students analyze six months of blog visitors with totals represented in expanded form, standard form, and written form. The students are asked, “How many visitors should Max expect to get on his blog site in one year?” Students complete a graphic organizer based on the presented data with the following prompts, “I know..., I need to find..., I can find the solution by....” Students then reflect upon their solution “I know my solution works...” (4.NBT.2 & 4.NBT.3)

In Lesson 27, Student Worktext, Session 2, Develop, Practice Comparing Decimals in Hundredths, Problem 1 states, “Shade and label the models to show .33 and .35. Then explain how the models show which decimal is less.” (4.NF.7)

In Interactive Practice, Understand Place Value, students reason about numbers and their relationships to determine the place value of a digit. (4.NBT.1)

In Interactive Practice, Divide Three Digit Numbers, students use tape diagrams and break apart numbers to understand how to divide three-digit numbers. (4.NBT.6)

Indicator 2b

Attention to Procedural Skill and Fluency: Materials give attention throughout the year to individual standards that set an expectation of procedural skill and fluency.

The instructional materials reviewed for Ready Classroom Mathematics Grade 4 meet expectations that they attend to those standards that set an expectation of procedural skill and fluency.

The materials include problems and questions, interactive games, and math center activities that develop procedural skill and fluency and provide opportunities for students to independently demonstrate procedural skill and fluency throughout the grade.

In Lesson 4, Session 2, Develop states, “Sam adds 6,152 and 379 and gets a sum of 9,942.” They must also explain why Sam’s addition is incorrect and find the correct sum of 6,152 + 379. Students develop procedural skills by connecting place value methods to use of the standard algorithm to add multi-digit whole numbers.

The instructional materials include Learning Games, interactive games to help build procedural skill and fluency, available in both English and Spanish, that can be accessed through i-Ready Reports. For example, Grade 4 students can play the game “Hungry Fish” which allows them to strengthen skills in the area of computation (4.NBT.4, 4.NBT.5). In this game, students are tasked with solving addition, subtraction, multiplication, or division problems using bubbles with parts of an equation and a fish with a corresponding solution.

4.NBT.4 (Fluently add and subtract multi-digit whole numbers using the standard algorithm) requires students to develop grade level fluency. This standard is addressed in several lessons in the Student Worktext, including:

In Lesson 4, Session 4, Refine, Apply It, Problem 1 states, “The population of Turtle Valley is 407,989. The population of Art Creek is 86,966. What is the total population of the two cities? Show your work.”

In Lesson 5, Session 4, Refine, Apply It, Problem 1 states, “What is the difference of 484,392 and 53,674? Show your work.” Students are expected to use the standard algorithm to solve the problem.

The instructional materials provide opportunities to independently demonstrate procedural skill and fluency throughout the grade-level. Within each lesson, there are Fluency and Skills Practice pages that children complete on their own. In addition, there are Learning Games and Math Center Activities that engage students with fluency practice. Examples of when students get opportunities to independently demonstrate procedural skill and fluency are:

In Lesson 5, Session 2, Develop, Practice Using Strategies to Subtract, Problem 2 asks students to “Find the difference. 16,407 - 9,524.” Students develop the procedural skill of subtraction of multi-digit whole numbers by connecting place value concepts to the standard algorithm. (4.NBT.4)

In Lesson 32, Fluency and Skills Practice, students practice adding and subtracting angles to make an angle of 180 degrees. (4.MD.7)

Math Center Activities are provided for students to work together in partnerships to develop procedural skill and fluency. In Lesson 4, Adding Whole Numbers, students develop procedural skills in adding and subtracting multi-digit whole numbers using the standard algorithm (4.NBT.4) in a game format with a partner. In the game Find Sums, students use a recording sheet containing two four-digit numbers, two five-digit numbers, and two six-digit numbers and a game board to solve addition problems such as, “4,376 + 1,337.” When students select a problem to solve and accurately solve it, they get to mark off the matching sum on the game board. When students have three numbers marked in a row, they win the game.

Indicator 2c

Attention to Applications: Materials are designed so that teachers and students spend sufficient time working with engaging applications of the mathematics, without losing focus on the major work of each grade

The instructional materials reviewed for Ready Classroom Mathematics Grade 4 meet expectations that the materials are designed so that teachers and students spend sufficient time working with engaging applications of mathematics. Engaging applications include single and multi-step problems, routine and non-routine, presented in a context in which the mathematics is applied.

Examples of opportunities for students to engage in routine application of mathematical skills independently and to demonstrate the use of mathematics flexibly in a variety of contexts in Classroom Resources include:

In Lesson 10, Session 3, Develop, Apply It, Problem 8 states, “Cadence shops for hiking gear. She picks out a $95 tent, a pair of boots for $54, and a $38 backpack. She has $200 to spend on gear. Write and solve an equation to find out if she has enough money for the hiking gear. Estimate to check that your answer is reasonable. Show your work.”

In Lesson 16, Fluency and Skill Practice, Problem 6 states, “Nora uses 80 inches of string to make a border for a rectangular painting. She wants the painting to have a width of 15 inches. What will be the length?”

In Lesson 20, Session 5, Refine, Apply It states, “Emily eats $$\frac{1}{6}$$ of a bag of carrots. Nick eats $$\frac{2}{6}$$ of the same bag of carrots. What fraction of the bag of carrots do Emily and Nick eat altogether?”

In Lesson 7, Math Center Activity, Multiplication and Division in Word Problems provides students with the opportunity to multiply or divide to solve word problems involving multiplicative comparison (4.OA.2). The materials state, “Flora buys 6 apples and 24 oranges. How many times as many oranges as apples does Flora buy?”

The instructional materials include multiple opportunities for students to engage in non- routine application of mathematical skills and knowledge of the grade level. For example, in Classroom Resources:

In Unit 2, Math in Action states, “The zoo is planning to build a new area for birds. The zoo is going to use recycled materials. There will be three different-size rectangular cages as shown below: Small cage: floor area of 12 square feet, Medium cage: floor area of 24 square feet, Large cage: floor area of 36 square feet. Beau needs to find a possible length and width for the rectangular floor of each size cage. What is a possible length, width, and perimeter for each cage’s floor?”

In Unit 4, Math in Action, Session 2 states, “Luna is designing a picture frame made out of craft sticks. Below are her instructions: Paint 6 craft sticks. Each stick is $$\frac{3}{4}$$ of an inch wide and $$5\frac{3}{4}$$ inches long. Glue the craft sticks side-by-side on a piece of cardboard. Glue a photograph $$2\frac{1}{4}$$ inches wide and $$2\frac{1}{4}$$ inches tall on the frame. Leave a space at least $$2\frac{2}{4}$$ inches wide of the right of the photo. You can put your decorations here. There needs to be at least $$\frac{2}{4}$$ of an inch of space above and below the photo. Explain if Luna’s plan works.”

In Unit 3, End of Unit, Unit Review, Performance Task states, “Zander expects 225 guests to be at the party. He plans on having 8 items in each goodie bag. Use the list of items below to put together an order for Zander. Explain how you know that your order has enough items.”

Indicator 2d

Balance: The three aspects of rigor are not always treated together and are not always treated separately. There is a balance of the 3 aspects of rigor within the grade.

The instructional materials reviewed for Ready Classroom Mathematics Grade 4 meet expectations that the three aspects of rigor are not always treated together and are not always treated separately. The instructional materials address specific aspects of rigor, and the materials integrate aspects of rigor.

All three aspects of rigor are present independently throughout the program materials. For example:

In Lesson 1, Session 2, Develop, Connect It, students develop conceptual understanding of place value. Problem 5 states, “What do the expanded form and a place-value chart tell you about a number such as 25,049? How are they alike and different?”

In Lesson 4, Session 4,Refine, students add multi-digit numbers using the standard algorithm. Problem 8 states, “Find the sum of 6,618 and 132,501. Then estimate to check that your answer is reasonable. Show your work.”

In Lesson 10, Session 4, Refine, students solve multi step word problems posed with whole numbers. Problem 2 states, “Taylor earns $5 each time she walks her neighbor’s dog. She has already earned $25. Write and solve an equation to find out how many more times Taylor needs to walk the dog to earn enough to buy a bike that costs $83. Check the reasonableness of your answer. Show your work.”

Multiple aspects of rigor are engaged simultaneously to develop students’ mathematical understanding of a single topic/unit of study throughout the materials. For example:

In the online game platform there are several opportunities for students to engage students in all three aspects of rigor: conceptual understanding, fluency and application. The game “Pizza” focuses on mental math and economic applications. Students use fluency and conceptual understanding to solve application problems related to costs associated with a pizza restaurant. Students set prices, compare vendors to find the best prices for pizza ingredients, and calculate the cost of customers orders.

In Lesson 21, Session 3, Develop, students use models to connect written procedures for subtracting mixed numbers in word problems. Problem 7 states, “Monica rides her bike $$3\frac{1}{4}$$ miles on Monday. She rides $$2\frac{2}{4}$$ miles on Tuesday. How much farther does Monica ride on Monday than on Tuesday? Show your work.”

Criterion 2e - 2g.iii

Practice-Content Connections: Materials meaningfully connect the Standards for Mathematical Content and the Standards for Mathematical Practice

The instructional materials reviewed for Ready Classroom Mathematics Grade 4 meet expectations for Practice-Content connections. Overall, the materials attend to the full meaning of the mathematical practices; however, there are instances where the practice standards are over-identified.

Indicator 2e

The Standards for Mathematical Practice are identified and used to enrich mathematics content within and throughout each applicable grade.

The instructional materials reviewed for Ready Classroom Mathematics Grade 4 partially meet expectations that the Standards for Mathematical Practice are identified and used to enrich mathematics content within and throughout the grade level.

In i-Ready, Teach and Assess, Ready Classroom Mathematics, Program Implementation, Standards for Mathematics in Every Lesson, The Standards for Mathematical Practice (MPs) are identified in each lesson along with information for how these MPs are addressed within the lessons. Specific information for an MP can be found in “Deepen Understanding” guidance for teachers. In addition, Discourse Questions, Structure and Reasoning, specifically related to MP7 (Look for and make use of structure) and MP8 (Look for and express regularity in repeated reasoning) and the Try-Discuss-Connect Instructional Routines all identify the MPs. In the document “Standards for Mathematical Practice in Every Lesson,” each lesson routine is outlined with the specific MPs that are addressed. Specifically, Try It focuses on MPs 1, 2, 4, 5, and 6, Discuss It focuses on MPs 2, 3, and 6, and Connect It focuses on MPs 2, 4, and 5. These routines are present in each lesson.

A “Correlations” document is also available in Program Implementation which includes “Standards for Mathematical Practices (SMPs) Correlation.” This table lists all eight Mathematical Practices, their corresponding descriptors, and the lessons where they can be found. A second table “Correlations by Ready Classroom Mathematics Lesson” provides a lesson by lesson listing of the MPs. In both tables, MPs 1 - 6 are identified as being present in all but one lesson, leading to an overidentification of these MPs. MP7 and MP8 are identified in specific lessons.

While these resources indicate a connection to the Standards for Mathematical Practice, the materials do not include a clear connection at the lesson and item level, in the teacher’s guide or student materials, as to how students are being explicitly taught and/or exposed to these standards. For example, in Lesson 14, the CCSS Focus in the Lesson Overview indicates that MP2, MP6, and MP7 are emphasized in the lesson. Teachers are referred back to Program Implementation, Standards for Mathematical Practice in Every Lesson, but there is no identification within lesson components for these MPs.

The Ready Classroom Mathematics Grade 4 instructional materials are structured so that the MPs enrich the content and are not treated as separate topics and/or activities. For example:

In Lesson 11, Session 2 students make use of structure (MP7) when relating expanded notation to the partial products method for multiplication to find “3 x 254= __.”

In Lesson 15, Session 2, students engage with MP1, “A factory has 2,125 tablets to ship to stores. It can ship 4 tablets in each box. How many full boxes can the factory ship?” Deepen Understanding connects this MP to develop an understanding of how a remainder affects the solution.

In Lesson 30, Session 3, students engage with MP5 when asked, “What else besides a sheet of paper could you use to perform this test?”

Indicator 2f

Materials carefully attend to the full meaning of each practice standard

The instructional materials reviewed for Ready Classroom Mathematics Grade 4 meet expectations that the instructional materials carefully attend to the full meaning of each practice standard. Overall, the materials attend to aspects of the mathematical practices (MPs) during different lessons throughout the grade, so when taken as a whole, the instructional materials attend to the full meaning of each MP.

In i-Ready, Teach and Assess, Ready Classroom Mathematics, Program Implementation, Standards for Mathematics in Every Lesson, includes information on how the Standards for Mathematical Practice (MPs) are addressed within each lesson, noting that key components of lessons are designed to engage students with the MPs. Deepen Understanding provides guidance for teachers on each MP within lessons sessions. Discourse Questions are included, as well as prompts for Structure and Reasoning specifically related to MP7 (Look for and make use of structure) and MP8 (Look for and express regularity in repeated reasoning). In addition, the Try-Discuss-Connect Instructional Routines all identify the MPs.

The instructional materials attend to the full intent of all eight Mathematical Practices. For example:

MP 1: Make sense and persevere in solving problems.

In Lesson 8, Session 3, Develop, Try It states, “Alfred is arranging 40 model cars into rows. He wants to put the same number of cars in each row. Find all the ways he can arrange the cars.” Teacher guidance states, “Make sense of the Problem: To support students in making sense of the problem, have them show that they recognize the need to find different ways that Alfred can arrange model cars in rows that have the same number of cars in each row.” Student Worktext, Discuss It states, “Ask your partner: How did you get started? Tell your partner: I started by...”

In Lesson 13, Session 2, Develop, Try It states, “Wanda is shopping for a pet carrier for her cat. One small carrier can hold 240 ounces. Her cat weighs 12 pounds. Can the carrier hold her cat?” Teacher guidance includes, “To support students in making sense of the problem, have them identify that the Customary Units of Weight table shows how pounds and ounces are related. Students may want to use the Math Reference Sheet as a reference for equivalent measurements of weight.”

In Unit 2, End of Unit, Unit Review, Performance Task states, “Melanie is in charge of setting up chairs for the Student Jazz Concert. She has 96 chairs to arrange in rows in a large classroom. She wants each row to have the same number of chairs. Find at least 6 different ways that Melanie can arrange the chairs. Choose one arrangement and explain why it does not make sense to use that arrangement. Then choose the arrangement that you think works best.” Students reason quantitatively when determining factor pairs for the six arrays, then reason abstractly when determining which factor pairs are most suitable for arranging the chairs.

MP 4: Model with mathematics.

In Unit 5, Math in Action, Session 2 states, “Bella is designing a wood mosaic piece. Angle Cuts: When Bella cuts pieces of wood for a project, she always saves the scraps. The scarps make good pieces for making mosaics. The cut pieces of different angle measurements. Bella sorts pieces by the angle measurements (angles are sorted into 30°, 45°, 50°, 60°, 80°, 90°, 100°, and 120°). Find a way Bella can put some pieces of wood together to make a 180° angle. Then measure and draw your angles to show that they make a straight line.” Reflect states, “Use a Model: What equations could you write to show the total measure of the angles you put together?”

In Lesson 29, Session 2, Develop, Apply It, Problem 7 states, “Lulu has 10 feet of ribbon. She uses $$1\frac{1}{3}$$ feet of ribbon for a project. She uses the rest of the ribbon to make bows. She uses 8 inches of ribbon for each bow. How many bows does Lulu make?” Students are to “Use what you have just learned to solve these problems.” Students can use equations, bar drawings, and/or number lines.

MP 5: Choose tools strategically.

In Student Worktext, Lesson 14, Session 3, Develop, Try It states, “There are 232 people waiting in line for an amusement park ride. Each car on the ride will be filled with 5 people. How many cars are needed to hold all the people waiting in line?” The Math Toolkit includes base-ten blocks, grid paper, and multiplication models for students to choose.

In Student Worktext, Lesson 26, Session 1, Explore, Try It, the Math Toolkit includes base-ten blocks, play money, hundredths grids, and index cards. Students choose tools to solve “Max has 248 pennies. How many whole dollars does Max have? What fraction of a dollar is left over?”

MP 6: Attend to precision.

In Lesson 16, Session 1, Explore, Support Partner Discussion, provides teachers with guidance for helping students attend to precision as they discuss, “Marissa uses 64 feet of fence to make a border around a rectangular flower garden. The length of the garden is 20 feet. What is the width of the garden? Encourage students to use the terms perimeter, width, and length as they discuss their solutions.”

In Unit 4, Unit Review, Performance Task states, “Ciara is using the recipe below to make 6 dozen cupcakes for a family party. She needs to buy flour, milk, and vanilla. Ciara also needs to buy boxes to carry the cupcakes to the party. Each box holds one layer of cupcakes. Ciara has $25 to spend. Does she have enough money to buy everything she needs to make the cupcakes and bring them to the party? Explain how you know.” The recipe and the prices for each ingredient are given. Reflect states, “Why is it important to use labels for all of the amounts while you are solving this problem?”

MP 7: Look for and make use of structure.

In Lesson 11, Session 2, Develop states, “What is the product of 3 and 254?” In Deepen Understanding, Partial Products, MP7 Make use of structure states, “When discussing partial products, prompt students to see that 3 x 254 can be written as 3 x (200 + 50 + 4) using the expanded form of 254. Ask: What idea that you learned can you use to find 3 x 254? Listen for: You can multiply each addend, 200, 50, and 4, by 3.” In this example, students use the structure of the distributive property to multiply a three-digit number by a one-digit number.

In Lesson 20, Session 2, Develop states, “Josie and Margo are painting a fence green. Josie starts at one end and paints 3/10 of the fence. Margo starts at the other end and paints 4/10 of it. What fraction of the fence do they paint altogether?” In Deepen Understanding, Number Line Model, MP7 Look for structure states, “When discussing the number line model, prompt students to consider how it could be used to demonstrate the commutative property. Generalize, Do you think this is true no matter what numbers you are adding? If you were using a number line to add 3 and 4, would it be true? Have students explain their reasoning. Listen for understanding that when adding whole numbers or fractions, the order of addends does not matter, the sum stays the same.”

MP 8: Look for and express regularity in repeated reasoning.

In Lesson 8, Session 2, Develop states, “Leona has 5 cups of oats. She needs 2 cups of oats for one full batch of oatmeal muffins. Can she use all of her oats by making multiple full batches of muffins?” In Deepen Understanding, Number Line Model, MP8 Use repeated reasoning states, “When discussing the number line model, prompt students to consider how it could be used to find multiples of another number, such as 3. Ask: How can you find multiples of 3 on the number line? Listen for: Start at 0 and skip-count by threes. Ask: What multiples of 3 do you see on the number line? Listen for: The multiples of 3 on the number line are 3, 6, and 9. Ask: How can you tell which number is a multiple of both 2 and 3? Listen for: A number that has both a circle and a box around it is a multiple of 2 and 3, so 6 is a multiple of 2 and 3.”

In Lesson 26, Session 2, Develop, Model It states, “You can use a place-value chart to understand how to write hundredths or tenths as a decimal. The place-value chart shows the value of 0.60.” Deepen Understanding states, ”When discussing the place-value chart, prompt students to consider how it helps them read the decimal and identify the place value of each digit.” It provides teachers with the questions, “What is the least place value of the number shown in the chart? What is the connection between the least place value and how you read the number? Do you think that you can always read a number in the place-value chart by the place value of the last digit shown?”

Indicator 2g

Emphasis on Mathematical Reasoning: Materials support the Standards' emphasis on mathematical reasoning by:

0/0

Indicator 2g.i

Materials prompt students to construct viable arguments and analyze the arguments of others concerning key grade-level mathematics detailed in the content standards.

In i-Ready, Teach and Assess, Ready Classroom Mathematics, Classroom Resources, the Student Worktext and the Math Journal provide students with opportunities to construct arguments and critique the reasoning of others. Evidence where students have opportunities to construct viable arguments includes:

In Lesson 7, Session 1, Try It, students solve a multiplication word problem and then justify their reasoning using the Discuss It prompt states, “Ask your partner: Do you agree with me? Why or why not? Tell your partner: I agree with you about… because…”

In Lesson 18, Session 4, Refine, a series of Pair/Share prompts in the margin of the materials help students construct viable arguments. The materials state, “How else could you solve this problem? Which strategy for comparing do you think works best with these fractions? How did you and your partner decide what strategy to use to solve the problem?”

Evidence where students have opportunities to analyze the mathematical arguments of others includes:

In Lesson 33, Session 3, Develop, Discuss It states, “Ask your partner: Do you agree with me? Why or why not? Tell Your Partner: I agree with you about...because…”

In Lesson 4, Session 3, Develop, Problem 5, students solve, “There is a mistake in the addition problem shown. Explain how the mistake was made. Then find the correct sum. 22,365 + 53,908 = 75,373"

Evidence where students constructing viable arguments and analyze the mathematical arguments of others includes:

Throughout the series there are dialogue boxes with the phrase, “Discuss It.” This dialogue box often encourages students to engage in discourse about the mathematics of the lesson. For example, in Lesson 7, Session 1, Explore, Try It, students solve the problem, “Hannah scored 3 goals last season. She scores 4 times as many goals this season. How many goals does Hannah score this season?” Discuss It, “Ask your partner: Do you agree with me? Why or Why not? Tell your partner: I agree with you because…”

Indicator 2g.ii

Materials assist teachers in engaging students in constructing viable arguments and analyzing the arguments of others concerning key grade-level mathematics detailed in the content standards.

In i-Ready, Teach and Assess, Ready Classroom Mathematics, Program Implementation, Resources include Discourse Cards which present questions and sentence starters to engage students in mathematical discourse, including the construction of arguments and analysis of others reasoning. For example, “Can you convince your partner or others that your answer makes sense? What do you think about what another student said? Does your partner’s strategy make sense? How is your solution method the same as or different from another student’s method?

In Classroom Resources, Lesson 0, Understanding the Try-Discuss-Connect Instructional Routine. The Discuss routine presents opportunities to use questions and sentence starters for students to share their thinking and critique each other’s reasoning. In addition, using Compare Strategies, students discuss how representations are the same, different, and related. For example, Lesson 0, Session 1, Discuss It, Compare Class Strategies states, “There are 236 third graders at Huron Elementary School. What is 236 rounded to the nearest hundred? Explain your reasoning.” Once students share strategies and reasoning, the teacher asks “How are they the same? How are they different? How are they connected?” These instructional routines are present in every lesson.

Evidence where the instructional materials support teachers to engage students in constructing viable arguments includes:

In Lesson 14, Session 3, Discuss It states, “There are 232 people waiting in line for an amusement park ride. Each car on the ride will be filled with 5 people. How many cars are needed to hold all the people waiting in line?” Teachers are prompted to ask such questions as, “Can you explain why you did it that way?”

In Unit 5, End of Unit, Unit Review, Performance Task, Reflect, has students reflect on their interpretations of logos they drew on grid paper matching a description. The materials state, “Argue and Critique: Suppose you ask your uncle to draw a log matching your description. Do you think his drawing will match what you had in mind? Explain your answer.” Teacher guidance about this section says, “Argue and Critique: Students should explain that there can be more than one figure that matches a given description.”

Evidence where the instructional materials support teachers to engage students in analyzing the arguments of others includes:

In Lesson 11, Session 1, Explore, Discuss It states, "What is the product of 3 and 57? Ask: How do (student name)'s and (student name)'s models represent 57 three times.

In Lesson 25, Session 2 states, “Carmen has $$\frac{4}{10}$$ of a dollar. Troy has $$\frac{50}{100}$$ of a dollar. Together, what fraction of a dollar do they have?” In Deepen Understanding, Models of Tenths and Hundredths, SMP3 Construct arguments and critique reasoning, states “Provide an opportunity for students to practice presenting their reasoning and critiquing the reasoning of others. Have several students present their reasons for representing Carmen and Troy’s money as they did. Ask: Why is your model or strategy a good way to show adding fractions with denominators for 10 and 100? Listen for: Responses should include specific advantages or strengths of students’ chosen model or strategy. Ask: What questions do you have about [student name]’s model or strategy? What do you think is helpful about the model or strategy [student name] used? What might be confusing or unclear in [student name]’s work using that model or strategy? Listen for: Responses should include clarifying questions and support identification of strengths and/or weaknesses of students’ models or strategies.”

Indicator 2g.iii

Materials explicitly attend to the specialized language of mathematics.

In i-Ready, Teach and Assess, Ready Classroom Mathematics, there are several resources to support teachers and students to use the specialized language of mathematics. In Program Implementation, the Academic Vocabulary Glossary identifies the vocabulary, provides a definition, and uses the word in a sample sentence organized by unit. For example, “Clarify, When you clarify a problem, you make it easier to understand”.

In Classroom Resources, Lesson Overview, Lesson Vocabulary identifies whether there is new vocabulary or review, and key terms used in the lesson. For example in Lesson 18, Session 2, vocabulary includes: “common denominator a number that is a common multiple of the denominators of two or more factors; denominator the number below the line in a fraction that tells the number of equal parts in the whole; numerator the number above the line in a fraction that tells the number of equal parts that are being described.”

Throughout lessons in Ready Classroom Mathematics, students are provided with Graphic organizers that assist with mathematical language to ensure students are using precise vocabulary. There are five different graphic organizers used throughout the lessons that allows students to organize learning concepts and vocabulary through definitions, illustrations, examples, etc. For example, Students Worktext, Lesson 14, Session 1 states, “Think about what you know about unknowns in equations. Fill in each box. Use words, numbers, and pictures. Show as many ideas as you can. Unknowns: In My Own Words, My Illustrations, Examples, Non-Examples.”

Build Your Vocabulary is provided at the beginning of each unit to support students in learning and using precise language and terminology. For example in, Unit 2, Beginning of Unit, Build Your Vocabulary, there are review vocabulary words, “array, equation, grouping, and factor.” The teacher’s guide provides suggestions for teachers to use with students to build math vocabulary using this page. It states “Display, point to, and read each review word aloud. Have students repeat chorally.” The page has diagrams for each word. The teacher’s guide states, “Have students work independently to label each word using the Review words. Pair students. Ask students to share their answers with their partners and explain how they decided which label to use. Observe and listen to students’ discussions to assess their understanding.”

In the Lesson Overview, Language Objectives are included for each lesson. For example, Lesson 8, Lesson Overview, Language Objectives, includes “Orally define and use in discussion the key mathematical terms factor, factor pair, multiple, composite number and prime number.”

In the End of Unit, Vocabulary, Vocabulary Cards are available. The materials state, “The purpose of the vocabulary cards is to reinforce students’ understanding of the new vocabulary words in the unit as well as to provide a place for students to record any other math words and definitions that would be helpful for them in their understanding of unit concepts. Students may find it useful to draw or write examples on the vocabulary cards as they encounter the terms during the unit. you may want to make a copy of the cards and display them in a word wall in the classroom to further support students’ learning.”

Gateway Three

Usability

Meets Expectations

Criterion 3a - 3e

Use and design facilitate student learning: Materials are well designed and take into account effective lesson structure and pacing.

The instructional materials reviewed forReady Classroom Mathematics Grade 4meet the expectations for being well designed and taking into account effective lesson structure and pacing. The instructional materials distinguish between problems and exercises, have exercises that are given in intentional sequences, have a variety in what students are asked to produce, and include manipulatives that are faithful representations of the mathematical objects they represent.

Indicator 3a

The underlying design of the materials distinguishes between problems and exercises. In essence, the difference is that in solving problems, students learn new mathematics, whereas in working exercises, students apply what they have already learned to build mastery. Each problem or exercise has a purpose.

There are several practice pages provided with each lesson. After receiving guidance from the teacher in the Try It section of each lesson, students can demonstrate their understanding in a variety of ways. Students solve problems to learn new mathematics in the Explore sessions of each lesson. These ideas are further developed in Develop sessions, where students solve problems in the Try It and Connect It sections. In the Refine session, students complete exercises where they apply their learning. For example:

In Grade 4, Lesson 23, Session 1, Explore, students use models to understand multiplication of fractions and whole numbers. In Session 2, Develop, students solve fraction multiplication by whole number problems using area models and number lines. In Session 3, Refine, students apply their learning in the Apply It session, where they solve word problems.

Indicator 3b

Design of assignments is not haphazard: exercises are given in intentional sequences.

The instructional materials reviewed forReady Classroom Mathematics Grade 4 meet expectations for designing assignments not being haphazard and exercises given in intentional sequences.

The sequence of lessons in each topic is designed to move from concrete and pictorial representation toward abstract work with numbers. Each unit has a Unit Flow and Progressions Video that highlights the work of the unit and how it fits in the progression of mathematics across grade levels.

Each unit also has a Learning Progression Chart that shows which lessons are building upon and which lessons students are preparing for within the unit. Each lesson has learning progression information which highlights work done in previous grade levels, as well as the work to be done in this lesson and subsequent lessons.

Each lesson has a consistent structure that builds towards independence. For example,

In Grade 4, Lesson 14, Session 2, Develop, the teacher is prompted to connect to prior knowledge of the relationship between multiplication and division. The teacher is prompted to help students make sense of the problem, “What is 136 ÷4?” Teachers are provided with possible prompts to support partner discussion such as, “How did you get started? What tools or models did you use?” During Connect It, the teacher leads a discussion to help students connect various models used. Finally, during Apply It and the Exit Ticket students practice and independently show their understanding.

Lessons within units build upon each other. For example:

In Grade 4, Unit 2 includes the following lessons and topics: Lesson 6: Understand Multiplication as a Comparison, Lesson 7: Multiplication and Division in Word Problems, Lesson 8: Multiples and Factors, Lesson 9: Number and Shape Patterns, and Lesson 10: Model and Solve Multi-Step Problems.

Indicator 3c

There is variety in what students are asked to produce. For example, students are asked to produce answers and solutions, but also, in a grade-appropriate way, arguments and explanations, diagrams, mathematical models, etc.

The instructional materials reviewed forReady Classroom Mathematics Grade 4 meet expectations for having a variety in what students are asked to produce.

Students are expected to respond to problems in a variety of ways, including produce answers, use models, drawings, and equations to support their explanations. Students are asked to justify their solutions with a partner and participate in discussions with Discuss It and Pair/Share prompts. Students respond to different problem types in the Refine section of the lessons, including short answer explanations, multiple choice, fill in the blank, and drawings. For example:

In Grade 4, Lesson 22, Session 4, Refine, students respond to problems in multiple ways when subtracting fractions in line plots. There are problems where students use tape diagrams, number lines, solve word problems, provide solutions with explanations, and solve multiple choice items.

Indicator 3d

Manipulatives are faithful representations of the mathematical objects they represent and when appropriate are connected to written methods.

Indicator 3e

The instructional materials reviewed forReady Classroom Mathematics Grade 4 meet the expectations for the visual design not being distracting or chaotic.

The student pages provide ample space for students to show work and write explanations. The layout of the lessons is consistent throughout all of the lessons and the student materials are present in the teacher edition. For example:

In Grade 4, Lesson 17, Student Worktext, Session 2, Develop, students use area models to show equivalent fractions. Rectangles are provided for students to show equivalent fractions. The graphics are clear and not distracting to the understanding of the concept

Criterion 3f - 3l

Teacher Planning and Learning for Success with CCSS: Materials support teacher learning and understanding of the Standards.

The instructional materials reviewed forReady Classroom Mathematics Grade 4 meet the expectations for supporting teacher learning and understanding of the Standards. The instructional materials support: planning and providing learning experiences with quality questions; contain ample and useful notations and suggestions on how to present the content; and contain explanations of the grade-level mathematics in the context of the overall mathematics curriculum.

Indicator 3f

Materials support teachers in planning and providing effective learning experiences by providing quality questions to help guide students' mathematical development.

The instructional materials reviewed for Ready Classroom Mathematics Grade 4 meet expectations for providing teachers with questions that are designed to elicit students’ mathematical understanding and thinking.

In Grade 4, Lesson 15, Session 2, Develop, questions are posed for the teacher to ask students. The questions are in italics and easy for the teacher to see. In Discuss It the following questions are provided: “How would you explain the strategy you used to solve the problem? Do you think your answer makes sense?”

Indicator 3g

Materials contain a teacher's edition with ample and useful annotations and suggestions on how to present the content in the student edition and in the ancillary materials. Where applicable, materials include teacher guidance for the use of embedded technology to support and enhance student learning.

The instructional materials reviewed for Ready Classroom Mathematics Grade 4 meets expectations for including ample notes and useful annotations and suggestions on how to present the content in the student edition.

The Program Implementation tab includes a “Digital Math Tools - Support Videos” section. This section includes support videos for counters and connecting cubes, base ten introduction, base ten: add and subtract, number line, multiplication models, perimeter and area, fraction models: add and subtract, and fraction models: compare and multiply.

In Classroom Resources, guidance for teachers supports the delivery of the content, as well as information on student responses for each section of the lesson. For example:

In Grade 4, Lesson 16, Session 2, Develop, the teacher notes include guidance for developing language. The materials state, “Develop Language Why: Support student understanding of the word edge as used in Apply It problem 7. How: Ask students to define or give examples of the word edge. Explain that the word edge is used informally to mean the end of an object. For example, students may sit on the edge of a rug or where the rug ends. In problem 7, edge refers to the side of a poster. Show students a poster and point to its edge.” This session also includes notes for common misconceptions, deepen understanding, and a hands-on activity if students are struggling.

Indicator 3h

Materials contain a teacher's edition (in print or clearly distinguished/accessible as a teacher's edition in digital materials) that contains full, adult-level explanations and examples of the more advanced mathematics concepts in the lessons so that teachers can improve their own knowledge of the subject, as necessary.

The instructional materials reviewed for Ready Classroom Mathematics Grade 4 meet expectations for containing a teacher’s edition that contains full, adult-level explanations and examples of the more advanced mathematics concepts in the lessons so that teachers can improve their own knowledge of the subject as necessary.

In Classroom Resources at the beginning of each unit, Learning Progressions, Math Background, and Unit Flow and Progression Videos provide information for teachers on mathematics and models. For example:

In Grade 4, Unit 4, Beginning of Unit, the Unit Flow & Progression video builds teacher understanding of how equivalent fractions in measurement and area are related to addition and subtraction from Grade 3, and leads to comparing fractions with unlike denominators, and how addition with mixed numbers can build on these underlying concepts.

Indicator 3i

Materials contain a teacher's edition (in print or clearly distinguished/accessible as a teacher's edition in digital materials) that explains the role of the specific grade-level mathematics in the context of the overall mathematics curriculum for kindergarten through grade twelve.

The instructional materials reviewed for Ready Classroom Mathematics Grade 4 meet expectations for containing a teacher’s edition that explains the role of the specific grade-level mathematics in the context of the overall mathematics curriculum for Kindergarten through Grade 12.

The Ready Classroom Mathematics materials include a “Learning Progression,” section in the teacher edition for each lesson that describes how the grade-level appropriate standard is developed in previous grades as well as how it will extend in the next grade. For example:

In Grade 4, Lesson 31, Full Lesson, Standards 4.MD.5 and 4.MD.6 are listed and defined. Under the Learning Progression section on the same page, which describes the progression students will learn about angles, it starts with in the previous lesson and moves to in this lesson and in the next lesson.

Indicator 3j

Materials provide a list of lessons in the teacher's edition (in print or clearly distinguished/accessible as a teacher's edition in digital materials), cross-referencing the standards covered and providing an estimated instructional time for each lesson, chapter and unit (i.e., pacing guide).

The instructional materials reviewed for Ready Classroom Mathematics Grade 4 contain an online portal that cross-references standards and provides a pacing guide for each lesson. Specifically, under the Program Implementation tab there are Teacher’s Guide, Table of Contents, Program Overview, Correlations, and Yearly Pacing resources to assist the teacher. Moreover, under the correlation resource there are correlations by state standard, correlations by ready classroom mathematics lessons, math in action correlations, standards for mathematical practices correlations, unit review correlations, and ELA standard correlations.

Indicator 3k

Materials contain strategies for informing parents or caregivers about the mathematics program and suggestions for how they can help support student progress and achievement.

The instructional materials reviewed forReady Classroom Mathematics Grade 4 contain strategies for informing parents or caregivers about the mathematics program and suggestions for how they can help support student progress and achievement. Family Letters for each lesson are found in the “Lesson Overview and Family Letter” tab at the beginning of each lesson. These letters explain the learning target and include an activity they can do at home. In the teacher edition, there is a “Connect to Family” section. For example:

In Grade 4, Lesson 21, the Family Letter provides parents with information about adding and subtracting mixed numbers and an activity for families to do with their child.

Indicator 3l

Materials contain explanations of the instructional approaches of the program and identification of the research-based strategies.

The instructional materials reviewed forReady Classroom Mathematics Grade 4 contain explanations of the instructional approaches of the program and identification of the research-based strategies. Under the Program Implementation Tab, there is a Supporting Research tab. Here, teachers can find supporting research charts including: “Ready Classroom Mathematicsis built on research from a variety of federal initiatives, national mathematics organizations, and experts in mathematics.” The chart lists instructional routines, mathematical practices, collaborative learning, and mathematical discourse. For each one of those items, the publishers have listed examples and corresponding research.

Criterion 3m - 3q

The instructional materials reviewed forReady Classroom Mathematics Grade 4meet expectations for offering teachers resources and tools to collect ongoing data about student progress on the Standards. The instructional materials provide opportunities for addressing common student errors and misconceptions, ongoing review and practice with feedback, clearly denote the standards being assessed, and provide rubrics and guidance for teachers to interpret student performance and suggestions for follow-up. The instructional materials also provide opportunities to gather information on students’ prior knowledge.

Indicator 3m

Materials provide strategies for gathering information about students' prior knowledge within and across grade levels.

The materials inReady Classroom Mathematicslist prerequisite skills for each lesson in the Lesson overview. Prerequisite Lessons are provided with each lesson to review concepts or to provide students with instruction in areas that may be gaps in their learning. For example:

In addition to identifying prerequisite skills for each lesson, Explore, at the beginning of each lesson, connects students’ prior knowledge with the content of the lesson. In some Warm-up questions there is a tag “Prerequisite” noting that the question is assessing prior knowledge.

The instructional materials include adaptive Diagnostic Assessments with Prerequisite Reports found in i-Ready, Reports.

Indicator 3n

Materials provide strategies for teachers to identify and address common student errors and misconceptions.

Indicator 3o

The instructional materials reviewed forReady Classroom Mathematics Grade 4 meet expectations for providing opportunities for ongoing review and practice, with feedback, for students in learning both concepts and skills.

Over the course of a lesson, which includes multiple sessions, materials engage students with multiple activities to review, practice, and independently demonstrate the grade-level mathematical concepts and skills.

Feedback is provided to students as they progress through the Sessions. Frequent feedback opportunities to address skills and concepts are provided in the Classroom Resources tab, within each lesson and its sessions. The Reteach - Tools for Instruction within each lesson provides teachers with sample errors and remediation strategies to address those errors. In addition, throughout the lesson sessions, potential misconceptions are highlighted with guidance for teachers to provide feedback and new opportunities for practice. For example:

In Grade 4, Lesson 14, Reteach Tools for Instruction, Divide Three-Digit by One-Digit Numbers, Check for Understanding states, “If you observe the student has trouble using multiplication facts to determine the missing factor, the student may have trouble recalling multiplication facts. Then try providing a multiplication fact table and instructing the student on how to use it.”

Standards are clearly noted within the assessments found at the end of each lesson. Standards are provided alongside the questions as well as the Depth of Knowledge level. Unit Assessment Correlations are available with the question number, DOK, Standard, and Lesson.

A Mid-Unit Assessment is provided for longer units. Mid-Unit Assessments also provide standards correlations for each item. These can be found in the Classroom Resources tab, End of Unit, Assess, Lesson Quizzes, and Unit Assessments.

Formative assessments are also available:

Lesson quizzes, exit tickets, and quick checks are provided for most lessons. These quizzes assess the specific standard(s) being taught in the lesson.

Within the sessions are Check For Understanding supports that include a statement as to why the check is being done. The why relates back to the standard being taught in the activities for that session.

Indicator 3p.ii

Assessments include aligned rubrics and scoring guidelines that provide sufficient guidance to teachers for interpreting student performance and suggestions for follow-up.

Rubrics are provided for Mid-Unit Assessments, Unit Assessments, Unit Performance Tasks, Lesson Quizzes, and Math in Action. (grade 2 and above) The rubrics and scoring guidelines support teachers to interpret student performance. Assessment answer keys are provided alongside the questions along with the DOK level for the item. For multiple choice answers, the correct answer and explanations for incorrect choices are given, including the most common misconceptions.

Reports from i-Ready diagnostic assessments and comprehension checks assist teachers in providing follow-up instruction for misconceptions and mathematical errors. The electronic reports also include links to assist in reteaching items missed. Within lessons, rubrics and scoring guidelines provide guidance for teachers to follow-up and, throughoutReady Classroom Mathematics, there is guidance for teachers on behaviors to look for, error alerts, and Common Misconceptions.

Unit Assessments include a Unit Assessment Teacher Guide that provides instructors with solutions, points possible, the exact standard covered, and the depth of knowledge (DOK) level for each item.

The Scoring Guide for the problems in the scoring table include: DOK, points of scoring, standard addressed, and lesson assessed by each problem.

The Scoring Rubrics includes points and expectations for short response, multiple select, choice matrix, extended response, and fill-in-the-blank items.

Assessment Practice provides some support for follow-up by identifying standards that need further study and reinforcement. Assessment Practice Answer Key and Correlations identify the standard which each question has been designed to evaluate.

Indicator 3q

The instructional materials reviewed forReady Classroom Mathematics Grade 4 encourage students to monitor their own progress.

Each Unit Opener has a Self-Check page for students to select the skills/concepts they think they already know and understand. End of Unit opportunities for self-reflection are provided at each grade level for all units. Assessments can be completed using an answer form that allows for students to correct the assessment orally after completion, review answers, and explain concepts students may not fully understand. Dialogue is fully supported inside the classroom to address student misconceptions and give students opportunities for both self- and peer assessment.

Criterion 3r - 3y

Differentiated instruction: Materials support teachers in differentiating instruction for diverse learners within and across grades.

The instructional materials reviewed forReady Classroom Mathematics Grade 4 meet the expectations for supporting teachers in differentiating instruction for diverse learners within and across grades. The instructional materials consistently provide: strategies to help teachers sequence and scaffold lessons; to meet the needs of a range of learners; tasks with multiple entry points; supports and accommodations for English Language Learners and special populations; and opportunities for advanced students to investigate mathematics content at a deeper level. The instructional materials provide a balanced portrayal of various demographic and personal characteristics, and include suggestions for grouping strategies.

Indicator 3r

Materials provide strategies to help teachers sequence or scaffold lessons so that the content is accessible to all learners.

The instructional materials reviewed forReady Classroom Mathematics Grade 4 meet expectations for providing strategies to help teachers sequence or scaffold lessons so that the content is accessible to all learners.

The sessions within a lesson follow the sequence of Explore, Develop, and Refine. Within a session, there is a sequence of Start, followed by Try It, Model It, or Apply It; Discuss; Connect; and Close.

Start is designed to build fluency or connect to prior knowledge.

Try It is designed to give students an opportunity to explore the concept on their own.

Model It is designed to allow students the opportunity to explore the concept through manipulatives or drawings.

Apply It is designed to give students an opportunity to practice the skill on their own.

Discuss is designed to allow students to talk to other students about the concept and compare what they did with each other.

Connect It is designed to help students connect the concept to real-life.

Close is designed to solidify the learning for the day and to check for understanding through the use of an exit ticket.

Each lesson includes a Differentiated Instruction Teacher Toolbox that includes Reteach (Tools for Instruction), Reinforce (Math Center Activities), and Extend (Enrichment Activities). For example, the Lesson 1 Overview states:

Reteach- “Children who require additional support for prerequisite or on-level skills will benefit from activities that provide targeted skills instruction.”

Reinforce- “Children who require additional practice to reinforce concepts and skills and deepen understanding will benefit from small group collaborative games and activities.” This is available in three versions: on-level, below-level, and above-level.

Extend- “Children who have achieved proficiency with concepts and skills are ready for additional challenges will benefit from group collaborative games and activities to extend understanding.”

Indicator 3s

Materials provide teachers with strategies for meeting the needs of a range of learners.

The instructional materials reviewed forReady Classroom Mathematics Grade 4 meet expectations for providing teachers with strategies to meet the needs of a range of learners.

Each lesson provides opportunity for differentiation in small group lessons, interactive digital tutorials, support for teachers to address common misconceptions at different points throughout lessons. For example:

The Differentiated Instruction opportunities provide support to reteach students who need additional support, reinforce learning for students who need additional practice, and extend learning for students who have achieved proficiency and are ready for further challenges.

The Language Development sections for English Language Learners provides even more differentiated support for students who are at different levels of English proficiency.

Community and Cultural Responsiveness activities build bridges between the mathematics students are learning to investigations of authentic contexts and issues. For example, students apply mathematics they have learned to objects and activities found in parks.

The materials also support learning with a variety of different experiences to develop connections in each lesson. For example:

Lessons use manipulative objects such as counters and connecting cubes for hands-on experiences where students are actively applying and representing mathematics with hands-on objects.

Partner and Whole group discussion are incorporated in all sessions to provide dialogue surrounding the mathematics being done.

Visual representations and physical representations using mathematics manipulatives are used throughout each session.

Indicator 3t

Materials embed tasks with multiple entry-points that can be solved using a variety of solution strategies or representations.

The instructional materials reviewed forReady Classroom Mathematics Grade 4 meet expectations for embedding tasks with multiple entry points that can be solved using a variety of solution strategies or representations.

The materials present word problems at the beginning of most lessons in the Try It part of the session, which provides multiple points of entry for students. During Model It, students can model the problem in whichever way they like. Examples of problems that provide multiple entry points, different representations, and/or solution pathways include:

In Grade 4, Lesson 27, Session 1, Explore, Try It states, “Kele and Kaci each buy equal-sized bottles of water. Kele now has 0.5 of his bottle left. Kaci has 0.4 of her bottle left. Who has more water left?”

Indicator 3u

Materials suggest support, accommodations, and modifications for English Language Learners and other special populations that will support their regular and active participation in learning mathematics (e.g., modifying vocabulary words within word problems).

The instructional materials reviewed forReady Classroom Mathematics Grade 4 meet expectations for suggesting support, accommodations, and modifications for English Language Learners and other special populations to engage students in regular and active participation in learning mathematics.

In Program Implementation, Implementation Support there are resources, including:

A Multilingual Glossary

A Bilingual Glossary

An Academic Vocabulary Glossary

WIDA PRIME V2 Correlation

Try-Discuss-Connect Routine Resources

In Classroom Resources, Teachers Edition, Language Development is identified for each lesson. This differentiated instruction chart provides guidance for teachers at three levels of differentiation that identifies specific strategies (e.g., Speaking/Writing, Reading/Writing) directly connected to lesson sessions and activities. During sessions, specific strategies target additional supports for students to support engagement in lesson activities. For example:

Prerequisite lessons are identified for most lessons and include specific supports for ELLs.

Develop Language includes Why (rationale for the suggestions) and How (strategies and guidance on how to engage students) sections, along with explanations as needed.

Discuss It provides supports for all students to engage in mathematical discourse.

Differentiated Instruction is included for most lessons and includes activities for intervention, on-level, and challenge.

Math Center activities provide multiple levels of content.

Math in Action lessons in Grade 2 and higher build background in a variety of contexts to ensure access for all.

Indicator 3v

Materials provide opportunities for advanced students to investigate mathematics content at greater depth.

The instructional materials reviewed forReady Classroom Mathematics Grade 4 meet expectations for providing opportunities for proficient and advanced students to participate in enrichment activities for a deeper challenge.

In i-Ready, Teach and Assess,Ready Classroom Mathematics, Classroom Resources, Teacher, Lesson Pacing Guide includes Small Group Differentiation Activities, and highlights Extend, Enrichment Activity. These Enrichment Activities can be found during the Refine session in the lesson, and include a Challenge Activity related to the content of the lesson. For example:

In Grade 4, In Lesson 31, Extend states, “Have students draw a circle using a compass. Have them draw a reflex angle with a measure of 200° by using a protractor to measure a 160° angle (360°- 160°= 200°) The larger angle formed measures 200°.”

Indicator 3w

Materials provide a balanced portrayal of various demographic and personal characteristics.

In the Program Implementation tab, a multilingual, bilingual, and academic glossary are provided. Throughout the materials there are examples of animated pictures of children that have varied skin tone, features, hair color, and hair types such as pictures of children with brown skin and black hair, light skin and blond hair, and brown skin and brown hair. Pictures with more than one child show interactions between children with varied skin and hair colors such as one with light brown skin and black hair and the other with dark brown skin and black hair. The pictures of objects included are pencils, cars, soccer balls, footballs, apples, bananas, crayons, goldfish, rocks, flowers and other objects commonly known to most students. A variety of names representing different ethnic and cultural backgrounds are used, including: Rosa and Ryan, Nick and Nora, Dave and Ari, Roberto and Rena, Fran and Pete, Gabe and Rose, Darious, Sam, Lexi, Paco, Julija, Lana, and Kyle.

Indicator 3x

Materials provide opportunities for teachers to use a variety of grouping strategies.

Each lesson session includes supports for partner discussion and whole class discussion. Some examples of discussions throughout the materials include: “Have pairs explain how they modeled and solved the problems. Compare and Connect the different representations and have children identify how they are related. Ask your partner: Do you agree with me? Why or why not? Tell your partner: I started by…” These discussion starters are used throughout the materials in all grades. Opportunities for grouping are also supported in the differentiated instruction and language development activities. The teacher materials offer support for whole class discussions and independent activities throughout the instruction.

Indicator 3y

Materials encourage teachers to draw upon home language and culture to facilitate learning.

The instructional materials reviewed forReady Classroom Mathematics Grade 4 provide support to draw upon home language and culture to facilitate learning. The materials offer a multilingual mathematics glossary that defines common mathematical terms in ten different languages. There are student discourse tools in both English and Spanish to support those two most common languages. There are family letters in Spanish, as well as in English, that support parents in learning mathematics at home.

Interactive Learning Games are available in English and Spanish.

Criterion 3z - 3ad

Effective technology use: Materials support effective use of technology to enhance student learning. Digital materials are accessible and available in multiple platforms.

The instructional materials reviewed forReady Classroom Mathematics Grade 4 integrate technology in ways that engage students in the Mathematical Practices. The digital materials are web-based and compatible with multiple internet browsers, and include opportunities to assess students’ mathematical knowledge and procedural skill. The digital materials do not include opportunities to personalize learning for students, but do present some opportunities for customization for local use. The instructional materials do not include opportunities for teachers and/or students to collaborate with each other.

Indicator 3z

Materials integrate technology such as interactive tools, virtual manipulatives/objects, and/or dynamic mathematics software in ways that engage students in the Mathematical Practices.

The materials include Interactive Tutorials with most lessons that are animated interactive lessons assigned to students in their personalized instructional plan. These tutorials include integrative technology such as interactive tools and digital math manipulatives to engage students in the Mathematical Practices.

Some lessons include multiple interactive tutorials related to the content of the lesson. Students work through the videos and answer questions. Students can use the lesson view to skip to different parts of the lesson. There is a pen for student use, as well as a notepad and a dictionary.

Digital Math Tools are provided to be used throughout the program. Tools available in the grades K-5 program include Counters, Connecting Cubes, Base Ten Blocks Tool, Number Line Tool, Multiplication Models Tool, Perimeter and Area Tool, and Fraction Models Tool. In general, tools are representative of concrete manipulatives.

Seven learning games are provided for student practice of concepts and skills. There is a document called “Learning Games Lessons Correlations” in the Program Implementation Guide, in the Digital Resource Correlations section, that provides information for teachers about which games support which lesson content.

Interactive Practice is provided for student practice of concepts. The practice is provided for some lessons but not all. In each Interactive Practice, students are given problems to solve which build on their conceptual understanding and help consolidate their knowledge.

Indicator 3aa

Digital materials (either included as supplementary to a textbook or as part of a digital curriculum) are web-based and compatible with multiple internet browsers (e.g., Internet Explorer, Firefox, Google Chrome, etc.). In addition, materials are "platform neutral" (i.e., are compatible with multiple operating systems such as Windows and Apple and are not proprietary to any single platform) and allow the use of tablets and mobile devices.

The instructional materials reviewed forReady Classroom Mathematics Grade 4 digital materials are web-based and compatible with multiple Internet browsers and operating systems. These materials also allow for the use of handheld and mobile devices. System requirements can be accessed by clicking the question mark at the top right-hand corner when signed in to the teacher website and clicking on the link to the system requirements PDF.

According to the PDF provided by the publisher, the materials are compatible with Windows 7 SP!, Windows 10 1802 (April 2018 update) or higher, MacOS X 10.11, MacOS 10.12-10.14, Google Chrome OS. Supported browsers include Internet Explorer on Mac and Google Chrome operating systems, Microsoft Edge, Microsoft Safari, Firefox, and Google Chrome. The publisher recommends Google Chrome with auto-updates enabled for the best experience. In addition, there is an app for iPads titled “i-Ready for Students.” The app is not supported for iPad minis. The app is not available for other tablets or the iPhone. However, when attempted, many of the tools can be viewed on other mobile devices through the website accessed through the browsers listed.

Indicator 3ab

Materials include opportunities to assess student mathematical understandings and knowledge of procedural skills using technology.

The instructional materials reviewed forReady Classroom Mathematics Grade 4 materials include online comprehension checks for each lesson. Comprehension checks have five problems and are a mixture of problem types, including multiple-choice, multiple select, fill in the blank, and drag and drop. Middle and End of Unit Assessments are also available for each unit in a digital version with similar formatting. Those assessments are customizable and allow teachers to eliminate or combine assessment items. The learning games offer teachers reports on three types of data that include time spent on activities, student performance on math skills, and other qualitative data such as student perseverance through difficult tasks. Reports for comprehension checks are available for individual students and at the class level.

Indicator 3ac

Materials can be easily customized for individual learners.
i. Digital materials include opportunities for teachers to personalize learning for all students, using adaptive or other technological innovations.
ii. Materials can be easily customized for local use. For example, materials may provide a range of lessons to draw from on a topic.

The instructional materials reviewed forReady Classroom Mathematics Grade 4 can be customized for individual learners or users through the digital platform using adaptive or innovative technologies.

In i-Ready, Assess and Teach, Assessment, teachers can customize Interactive Practice assignments. In i-Ready, Reports, Learning Games can also be customized. i-Ready Instruction, available for an additional purchase, includes additional opportunities to customize content. In i-Ready, Assess and Teach, Classroom Resources, Lesson Quizzes, Fluency and Skills activities, and powerpoint slides for each lesson are customizable.

The instructional materials reviewed forReady Classroom Mathematics Grade 4 materials provide limited opportunities for teachers to customize lessons for local use.Ready Classroom MathematicsTeacher Resources include Small Group Differentiation using Prerequisite Lessons, Tools for Instruction, Math Center Activities, and Enrichment Activities. These are teacher-led activities for use with small groups requiring additional instruction and/or review prerequisite concepts. Middle and End of Unit Assessments have one editable form, digital assessments are customizable, and fluency pages have an editable form as well.

Indicator 3ad

Materials include or reference technology that provides opportunities for teachers and/or students to collaborate with each other (e.g. websites, discussion groups, webinars, etc.).

The instructional materials reviewed forReady Classroom Mathematics Grade 4 provide no explicit guidance for opportunities for collaboration using technology. No opportunities are provided for teacher-to-student collaboration or student-to-student collaboration. There are no technical features that allow collaboration between teacher and student or between students.

About Publishers Responses

All publishers are invited to provide an orientation to the educator-led team that will be reviewing their materials. The review teams also can ask publishers clarifying questions about their programs throughout the review process.

Once a review is complete, publishers have the opportunity to post a 1,500-word response to the educator report and a 1,500-word document that includes any background information or research on the instructional materials.

Educator-Led Review Teams

Each report found on EdReports.org represents hundreds of hours of work by educator reviewers. Working in teams of 4-5, reviewers use educator-developed review tools, evidence guides, and key documents to thoroughly examine their sets of materials.

After receiving over 25 hours of training on the EdReports.org review tool and process, teams meet weekly over the course of several months to share evidence, come to consensus on scoring, and write the evidence that ultimately is shared on the website.

All team members look at every grade and indicator, ensuring that the entire team considers the program in full. The team lead and calibrator also meet in cross-team PLCs to ensure that the tool is being applied consistently among review teams. Final reports are the result of multiple educators analyzing every page, calibrating all findings, and reaching a unified conclusion.

Rubric Design

The EdReports.org’s rubric supports a sequential review process through three gateways. These gateways reflect the importance of standards alignment to the fundamental design elements of the materials and considers other attributes of high-quality curriculum as recommended by educators.

Advancing Through Gateways

Materials must meet or partially meet expectations for the first set of indicators to move along the process. Gateways 1 and 2 focus on questions of alignment. Are the instructional materials aligned to the standards? Are all standards present and treated with appropriate depth and quality required to support student learning?

Gateway 3 focuses on the question of usability. Are the instructional materials user-friendly for students and educators? Materials must be well designed to facilitate student learning and enhance a teacher’s ability to differentiate and build knowledge within the classroom. In order to be reviewed and attain a rating for usability (Gateway 3), the instructional materials must first meet expectations for alignment (Gateways 1 and 2).

Key Terms Used throughout Review Rubric and Reports

Indicator Specific item that reviewers look for in materials.

Criterion Combination of all of the individual indicators for a single focus area.

Gateway Organizing feature of the evaluation rubric that combines criteria and prioritizes order for sequential review.

Alignment Rating Degree to which materials meet expectations for alignment, including that all standards are present and treated with the appropriate depth to support students in learning the skills and knowledge that they need to be ready for college and career.

Usability Degree to which materials are consistent with effective practices for use and design, teacher planning and learning, assessment, and differentiated instruction.

Math K-8 Rubric and Evidence Guides

The K-8 review rubric identifies the criteria and indicators for high quality instructional materials. The rubric supports a sequential review process that reflect the importance of alignment to the standards then consider other high-quality attributes of curriculum as recommended by educators.

For math, our rubrics evaluate materials based on:

Focus and Coherence

Rigor and Mathematical Practices

Instructional Supports and Usability

The K-8 Evidence Guides complement the rubric by elaborating details for each indicator including the purpose of the indicator, information on how to collect evidence, guiding questions and discussion prompts, and scoring criteria.

K-8 Math

The EdReports rubric supports a sequential review process through three gateways. These gateways reflect the importance of alignment to college and career ready standards and considers other attributes of high-quality curriculum, such as usability and design, as recommended by educators.

Materials must meet or partially meet expectations for the first set of indicators (gateway 1) to move to the other gateways.

Gateways 1 and 2 focus on questions of alignment to the standards. Are the instructional materials aligned to the standards? Are all standards present and treated with appropriate depth and quality required to support student learning?

Gateway 3 focuses on the question of usability. Are the instructional materials user-friendly for students and educators? Materials must be well designed to facilitate student learning and enhance a teacher’s ability to differentiate and build knowledge within the classroom.

In order to be reviewed and attain a rating for usability (Gateway 3), the instructional materials must first meet expectations for alignment (Gateways 1 and 2).

Alignment and usability ratings are assigned based on how materials score on a series of criteria and indicators with reviewers providing supporting evidence to determine and substantiate each point awarded.

For ELA and math, alignment ratings represent the degree to which materials meet expectations, partially meet expectations, or do not meet expectations for alignment to college- and career-ready standards, including that all standards are present and treated with the appropriate depth to support students in learning the skills and knowledge that they need to be ready for college and career.

For science, alignment ratings represent the degree to which materials meet expectations, partially meet expectations, or do not meet expectations for alignment to the Next Generation Science Standards, including that all standards are present and treated with the appropriate depth to support students in learning the skills and knowledge that they need to be ready for college and career.

For all content areas, usability ratings represent the degree to which materials meet expectations, partially meet expectations, or do not meet expectations for effective practices (as outlined in the evaluation tool) for use and design, teacher planning and learning, assessment, differentiated instruction, and effective technology use.